A note on logarithmic convergence rates for nonlinear Tikhonov regularization

DOI10.1515/jiip.2008.006zbMath1154.65042OpenAlexW1998576706MaRDI QIDQ5451999

Barbara Kaltenbacher

Publication date: 27 March 2008

Published in: jiip (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jiip.2008.006

zbMATH Keywords

convergenceHilbert spaceill-posed operator equationTikhonov regularizationnonlinear operator equations

Mathematics Subject Classification ID

Nonlinear ill-posed problems (47J06) Numerical solutions to equations with nonlinear operators (65J15) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20)

Related Items (14)

Newton-type iteration for Tikhonov regularization of nonlinear ill-posed problems ⋮ An extension of the variational inequality approach for obtaining convergence rates in regularization of nonlinear ill-posed problems ⋮ Conditional stability versus ill-posedness for operator equations with monotone operators in Hilbert space ⋮ Tikhonov regularization with oversmoothing penalty for non-linear ill-posed problems in Hilbert scales ⋮ Simplified iteratively regularized Gauss-Newton method in Banach spaces under a general source condition ⋮ Regularization Methods for Ill-Posed Problems ⋮ On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems ⋮ Newton type iteration for Tikhonov regularization of non-linear ill-posed Hammerstein type equations ⋮ Expanding the applicability of a modified Gauss-Newton method for solving nonlinear ill-posed problems ⋮ Levenberg-Marquardt method with general convex penalty for nonlinear inverse problems ⋮ About a deficit in low-order convergence rates on the example of autoconvolution ⋮ Modern regularization methods for inverse problems ⋮ Variational Source Conditions in $L^p$-spaces ⋮ On convergence of regularized modified Newton's method for nonlinear ill-posed problems

Cites Work

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• On the regularization of nonlinear ill-posed problems via inexact Newton iterations
• Optimal a Posteriori Parameter Choice for Tikhonov Regularization for Solving Nonlinear Ill-Posed Problems
• Factors influencing the ill-posedness of nonlinear problems
• On convergence rates for the iteratively regularized Gauss-newton method
• Regularizing properties of a truncated newton-cg algorithm for nonlinear inverse problems
• Regularization of exponentially ill-posed problems
• Tikhonov regularization anda posteriorirules for solving nonlinear ill posed problems
• Convergence of projected iterative regularization methods for nonlinear problems with smooth solutions

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